A start-up apparatus for a power supply is presented. A charging path from an input voltage to a holding capacitor is cut off after the power converter starts up. The start-up apparatus includes a transistor having a drain supplied with the input voltage, and a source connected to the holding capacitor and an input of a start-up control unit. An output of the start-up control unit controls a switch and the transistor. The holding capacitor starts to be charged as the transistor is turned on. Once a voltage across the holding capacitor exceeds a start-up voltage, an internal control circuit is powered via the switch. Meanwhile, the transistor is turned off and the charging path is cut off. Furthermore, the start-up apparatus provides a hysteresis threshold voltage range for controlling the power converter.